Slovic (1962)

• “…future research must carefully consider the problem of adequately defining and assessing risk taking behavior.”

This talk

• Part 1: a destination
  • what are risk attitudes?
  • how do we measure them?
• Part 2: a map
  • a detailed map of elicited risk attitudes
  • an assessment of convergent and predictive validity*
• Part 3: finding one’s way
  • task-specific bias
  • risk perception

Measuring risk attitudes

A difficult task with crucial relevance

• directly unobservable
• latent construct (\(\Rightarrow\) requires a theory)
• should we..
  • infer from real world data or from ad-hoc choices
  • ask or task?
  • elicit by descrption or by experience?

and by the way, what is risk?

Risk in psychology

The act of implementing a goal-directed option qualifies as an instance of risk taking whenever two things are true: (a) the behavior in question could lead to more than one outcome and (b) some of these outcomes are undesirable or even dangerous. In essence, then, risk taking involves the implementation of options that could lead to negative consequences.

(Byrnes et al 1999)

The state of the art: psychology

risk loosely defined as probability of harm

focus on questionnaires and intuitive tasks

• Quests:
  • directly ask
  • over different domains
  • tackle risk perception
• Tasks
  • putting the subject in a ‘risky’ situation
  • card/gambling tasks

Metrics of success: convergent validity + predictive validity

Risk in economics

decisions given a probability distribution over outcomes

• if probability and outcomes known: risk

• if only oucomes known: ambiguity

• if both unknown: knightian uncertainty

The EUT framework

The EUT framework

The EUT framework

The EUT framework

The state of the art: economics

risk formally defined as uncertainty over outcomes

focus on decontextualized tasks (and questionnaires)

• The lottery paradigm
  • incentives
  • risk task = choice over lotteries
  • different formats, cover stories, contexts
  • strong theoretical underpinning
  • estimation of utility functions (\(\Rightarrow\) models)

Metric of success: internal validity (task \(\iff\) theory)

Holt and Laury

Binswanger / Eckel and Grossmann

Bomb Risk Elicitation Task

Investment Game (Gneezy and Potters)

Balloon Analog Risk Task (Lejuez et al)

Certainty Equivalent MPL

Questionnaire: SOEP

How likely are you to take risks in general, one a scale from 0 (not taking any risks) to 10 (taking many risks)?

Questionnaire: DOSPERT

Domain Specific Risk Taking Scale

• 6 domains: investing, gambling, health/safety, recreational, ethical, and social
• 1 to 7 scale: how risky do you think X is?
• 1 to 7 scale: how likely are you to engage in X?

Examples:

• Riding a motorcycle without a helmet.
• Engaging in unprotected sex.
• Investing 10% of your annual income in a moderate growth diversified fund.

METARET

A meta-analysis of Risk elicitation tasks

• elicited risk atitudes: tasks and questionnaires

• convergent validity: correlation among tasks

• convergent validity: correlation among questionnaires

• predictive validity: correlation task \(\iff\) questionnaires

METARET resources

• your data (thanks!)

• preregistration on OSF

• transparent data collection & analysis on gitHub

• live data exploration on a shiny app

Contributors (so far: 17.321 subjects)

• Gnambs Appel and Oeberst (PONE 2015)
• Crosetto and Filippin (EXEC 2016)
• Filippin and Crosetto (ManSci 2016)
• Pedroni Frey Bruhin Dutilh Hertwig and Rieskamp (NHB 2016)
• Menkhoff and Sakha (JEconPsy 2017)
• Frey Pedroni Mata Rieskamp and Hertwig (ScAdv 2017)
• Nielsen (JEBO 2019)
• Charness Garcia Offerman and Villeval (WP 2019)
• Holzmeister and Stefan (WP 2018)
• Zhou and Hey (ExEc 2018)
• Fairley Parelman Jones and McKell Carter (JEconPsy 2018)
• Csermely Rabas (JRU 2018)

Assumptions: CRRA (à la Wakker)

\(u(x) = x^r\)

• simple
• captures risk aversion
• makes different tasks comparable

CRRA

How big are the differences?

elicited attitudes: summary

• low consistency across tasks

• surprisingly, low consistency also within tasks

• but heterogeneity by task is large

• only result that holds: most people are risk averse

possible explanation: between-subjects variation.

Questionnaires: summary

• better consistency across samples

• a tendency to report ‘in the middle’

• we do not really know what those numbers mean

Convergence: more evidence

Convergence: summary

• we replicate Slovic 1962 (!!)

• no correlation higher than .35

• when transalitng into r things get worse

Predictive validity: more evidence

Predictive validity: summary

• low correlations with questionnaires

• across questionnaires and tasks

• Beauchamp et al JRU 2016: questionnaires are rather predictive

Finding one’s way

• task-specific bias

• noise

• risk perception

• theory

Finding one’s way

• task-specific bias

• (noise)

• risk perception

• (theory)

what if tasks distort choices?

noisy preference + one-shot choices \(\Rightarrow\) noisy data

• cognitive limits \(\Rightarrow\) limited understanding

• task-specific bias?

(this work: Crosetto and Filippin, ExEc 2015)

Simulations

How does the mere mechanics of each task affect the outcome?

Simulation exercise:

• generate 100k virtual agents
• for each agent, \(r\sim N(0.7,0.3)\)
• let the agents play each of the 4 tasks
• collect results, run statistics
• analyze the retrieved \(\hat{r}\)

A good task should be able to recreate the starting distribution, if no error.

Deterministic vs noisy

3 types of simulations:

• deterministic

• random parameter model \(\Rightarrow\) models fuzzy preferences

  • for each agent, \(r = r_0 + \varepsilon, \; \varepsilon \sim \mathcal{N}(0,\mu)\)
  • \(\mu \in (0.3;0.6)\)

• random agents \(\Rightarrow\) models frame effects

  • 10% of subjects act randomly on the space of the task

Starting distribution

HL

HL

HL

EG

EG

EG

GP

GP

GP

BRET

BRET

BRET

Task-specific summary

is there a task-specific bias? yes

does it account for all differences? no

is this the only way to take noise into account? no

Risk perception

Risk perception: a mismatch

• economists assume subjects share the same risk definition

• namely:

  • risk as a distribution of probability over outcomes
  • \(EV\) as the average across all possible states of the world
  • risk aversion as diminishing marginal utility of money
  • subjects care about variance

• but subjects think of risk as probability of a loss

• do subjects find our tasks risky?

• We do not know because we assume they do

Experimenting on risk perception

• Holzmeister et al Working Paper
• gave description of return from an asset to subjects
• \(\sim\) 7000 subjects
• including \(\sim\) 2500 traders
• asked to rate perceived risk of each asset

Holzmeister et al: design

results - skewness

results - aggregate risk measures

Have we got the right theory?

Have we got the right theory?

Other theories

• Spiliopoulos & Hertwig: different decision rules for different contexts
• Schneider and Sutter: higher moments matter
• Sunder et al: curvature of utility function not a valid theory
• Ergodicity economics (Peters et al): drop EV, use time-means
• …

Summing up…

• “…future research must carefully consider the problem of adequately defining and assessing risk taking behavior.”

• exactly as in 1962

Contribute to the meta-analysis!

if:

• you have run a RET
• you have run more than one
• you have run a RET and a questionnaire
• you have run a RET and another risk-related measure

then:

send your data – paolo.crosetto@inrae.fr

github: (https://github.com/paolocrosetto/METARET)

shiny app: (https://paolocrosetto.shinyapps.io/METARET/)